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JEE Main 202224 JuneEvening Shift

Exam: JEE Main
Year: 2022
Date: 24 June
Shift: Evening Shift
Subject: Mathematics
Chapter: Parabola

JEE Main 2022 · 24 June · Evening Shift · Mathematics · Parabola

Let P _ 1 be a parabola with vertex (3, 2) and focus (4, 4) and P _...

Let

{P}_{1}

be a parabola with vertex \left(3, 2\right)

and focus \left(4, 4\right) and {P}_{2}

be its mirror image with respect to the line

x + 2y = 6

. Then the directrix of

{P}_{2}

is

x + 2y =

_____.

Let P _ 1 be a parabola with vertex (3, 2) and focus (4, 4) and P _ 2 be its mirror image with respect to the line x +

Correct answer

0

Step-by-step solution

Plotting the diagram as per given data we get,

Let P _ 1 be a parabola with vertex (3, 2) and focus (4, 4) and P _ 2 be its mirror image with respect to the line x +

${P}_{1}$ : Directrix

$x + 2y = k$

$x + 2y - k = 0$

\left|\dfrac{3 + 4 - K}{\sqrt{5}}\right| = \sqrt{5} $</p><p>\left|7 - k\right| = 5$

$\begin{cases}7 - K = 5 & 7 - K = - 5 \\ k = 2 & k = 12 \\ Accepted & RejectedPassesthroughfocus\end{cases}$

\left $\begin{array}{ll}{D}_{1} = x + 2y = 2 \\ = x + 2y = 6 \\ {D}_{2} = x + 2y = C\end{array}$ $\right] ⇒ d ⇒ d ⇒ c = 10

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